Capacity Collaboration in Semiconductor Supply Chain with Failure Risk and Long-term Profit 191 ,i j f The failure risk that use product i to satisfy demand j. ,i j α Contribution margin for satisfying a demand of class j with product i. t The customer type, t=1,2,or3. () t jj f r Customer lifetime value of customer j type t. r j The quantity of the realized demand class j. h i The holding cost of product i per unit. ()QΠ The total profit of the integrated supply chain. a 1 , b 1 , a, b, a 2 , b 2 The constants in CLV function 3.3.1 The customer lifetime value In marketing, customer lifetime value (CLV) is the present value of the future cash flows attributed to the customer relationship. Use of customer lifetime value as a marketing metric tends to place greater emphasis on long-term customer satisfaction, rather than on maximizing short-term sales. CLV is directly influenced by customer satisfaction, which is positively related to the fulfil rate of the demand. The customer satisfaction is an inside feeling, so it may be different among individuals. We assume that U j =f j (r j ) based on utility curves theory (Becker et al. 1964), where r j denotes fulfil rate of demand j. The CLV curve is depicted in the following figure. Fig. 5. Relationship between demand fulfil rate and CLV value In figure 5, curve 1 denotes the CLV of positive customer, curve 2 demotes the CLV of neutral customer and curve 3 denotes the CLV of conservative customer. It is obviously that the CLV values are identical among all types of customers when their demands are fulfilled. The probability of the customer j is belongs to type t is t j k (t=1,2,3), so 1 t j i k = ∑ . We assume the CLV functions 123 (), (), () jj jj jj f r f r f r along with customer types based on the utility curves theory (Becker et al. 1964). The functions equal to 11 22 ,, jj rr j abeabrabe−++ , respectively, and the parameters a, b, a 1 , b 1 , a 2 , b 2 are constants. The functions have the following relationships: 123 jjj f (1) = f (1) = f (1) = 0 and 123 jjj max f (1) = f (1) = f (1)=U . If j 01,r<< we have 123 jj jj jj f (r ) > f (r ) > f (r ) . Supply Chain Management 192 j j r 11 jj j r 22 a - b e (neutral customer ,t = 1) f (r ) = a + br (positive customer ,t = 2) a + b e (conservative customer,t = 3) ⎧ ⎪ ⎪ ⎨ ⎪ ⎪ ⎩ 3.3.2 The failure risk cost System failure risk is often happened in the semiconductor supply chains, and they always result to great capital losses. Failure risks of the stochastic manufacture system mainly come from the equipment failure, the shipping failure in transport, or the high technology demands. In the system, there is always a probability that each piece of ordered product will not be supplied to the customer. In this chapter, we use f ij to describe the probability of the failure of one unit of product shipment: use product i to satisfy the demand class j. If we planed to use product i to satisfy the demand j for q piece, the expect failure cost of the supplement is qf ij . 3.3.3 Other costs and revenues In the manufacture and allocation system, the material supplier must buy the materials from the outside of the system. Then, the manufacturing process starts, the manufacturers spent the consumables to conduct manufactures. If the products are not fully sold, it will be hold in stock and allocate in the next selling period. The fulfilled demand will increase the customer life time value, because the fulfilled customer may suggest others to purchase or will maintain the bought products. When the demands are not fulfilled, the retailer should pay the shortage cost to the customers. So, on the view of the integrated system, the other costs are the material cost, holding cost, shortage cost. At the same time, the system gains the revenue from products’ selling. 3.3.4 Model constraints The system faces some constraints. For example, the demand constraint: the supplied quantity to a certain demand should not exceed the need, that is, ,i j i i y d ≤ ∑ . At the same time, all the realized demand fulfilled by the one type of product should not exceed the total quantity in inventory, that is, ,i j ii i i y eQ I ≤ + ∑ . 3.3.5 Model construction Generally, higher classes of products have higher revenue and usage costs, so it is reasonable that the revenue ( p j +v j ) and usage cost u j decrease with the index j . Then we have: jj ii p v p v + >+ , j i uu> for ji < (1) ,, / i jjj i j i j i p vuU y α =+−+ ∑ , (2) Let ()QΠ be the profit function of the supply chain in the whole manufacturing and selling rotation. In the production stage the supplier determines the optimal material quantity that will be input in the manufacturing system, then, varieties products are manufactured and Capacity Collaboration in Semiconductor Supply Chain with Failure Risk and Long-term Profit 193 shipped to the customers under a proper allocation policy. Our objective is to determine the optimal material quantity and the capacity of each manufacturer in order to maximize the profit function. We formulate this problem as a programming model, and it is as follows: 1 ,, ,, , , , , , () max[( ) ( )] t nj i j i j ii j i j i j iii i i j ddk ij i j j QE y vdUCQfyheQIy α Π= − + −− − +− ∑∑∑ ∑ (3) Where, () t jjjj Uk f r= (4) 11 22 (neutral customer, 1) ( ) (positive customer, 2) (conservative customer, 3) j j r jj j r abe t fr abr t abe t ⎧ −= ⎪ ⎪ =+ = ⎨ ⎪ + = ⎪ ⎩ , j i j i r y = ∑ (5) ,i j i i y d ≤ ∑ (6) ,i j ii i j y eQ I ≤ + ∑ (7) i i QQ= ∑ (8) max (0) 0, (1) tt jj ffU== (9) , , , , (1,2, , ) ij i y QRi j n + ∈∈ ()QΠ in equality (3) includes five parts: the total profit in the allocation stage, the CLV value, the material and manufacturing cost, the expected failing risk cost, and the holding cost of the residual products. 1122 ,, , , , , i aba b a b Iand max U are constants. ,i j f is the failure risk of one unit of product i, which is used to fulfil demand j, so , 01 ij f ≤ ≤ . Equalities (4) and (9) are the CLV function and the corresponding restraint. Equality (5) is the fulfilled demand i. Inequalities (6) and (7) are the demand constraint and supply constraint, respectively. Equality (8) states that all the materials are allocated to manufacturers. 4. Model analysis Substitution in semiconductor industry is very common in practice, because the nature performance of the same type of products even in one batch may be different. But the practice is always hard to describe in mathematical modelling, little has been done on the impact of the demand substitution to the supply chain network. Substitution can help to Supply Chain Management 194 remit the bullwhip effect and gives the supply chain with flexibility. A number of papers have studies substitution policy in a product allocation system (Chen & Plambeck, 2008; Shumsky & Zhang, 2009). The dissertation applies and studies the impact of the demand substitution to a semiconductor supply chain network. In this manufacture and allocation system, the whole rotation can be divided into two stages: the production stage and the allocation stage (see figure 1). At the production stage, the supplier determines the optimal materials input, while at allocation stage the manufacturers allocate the products. The allocation policy determines not only the revenue of the allocation stage, but also the materials inputs at the production stage. Let N be the difference between the actual demand and available product, then we have: 12 11 1 1 22 2 2 ( , , , ) (( ),( ), ,( )) nnnnn NNNN eQIdeQId eQId==+−+−+− Obviously, ( 1, , ) i Ni n= can be positive, negative, or zero. For 1, ,in = , if 0 t i N > and 0 t j N < , then ,i j y units of product i can be offered for upgrading. The realized upgraded quantity is non-negative and does not exceed the quantity that product i can provide. That is, , 0min(,) i jj i y NN≤≤ Single-step upgrade can deliver most of benefit of more complex substitution schemes (Jordanand 1995) and some literatures consider the single-step upgrade as the optimal allocation policy (Shumsky & Zhang, 2009). The single-step upgrade allocation policy states that the substitution can be allowed between two neighbour product classes where the high class products are in stock (see figure 6.). Fig. 6. Single step upgrade substitution Proposition 1. Traditional substitution policy is not the optimal allocation policy of the integrated system. In our paper, we take customer life time value in to account as one evaluation indicator when make allocation decisions. When 0, 0 tt ij NN><, i<j, and 1 0, t j N + < we may choose the residual quantity product i to satisfy the demand class of j or demand class j+1 or even both the demands, but the puzzle is that which is the optimal choice of the three substitution policies. Based on equation (2), the difference between contribution margin ,i j α and contribution margin ,1i j α + are, Capacity Collaboration in Semiconductor Supply Chain with Failure Risk and Long-term Profit 195 ,,1 ,11 1,1 11 ,1,1 (/)( /) ()(//) ij ij i i j j ij i i j j ij ii ii ii j ij j ij ii pvuU y p v uU y pp vv U y U y αα α + ++ + + ++ ++ Δ= − =+−+ − + −+ =− +− + − ∑∑ ∑∑ (10) In equality (10), α Δ consists of two part, the first part 11ii ii p pvv + + − +− is obviously positive because of equality (1). The values of , / j i j i U y ∑ and 1,1 / j i j i Uy + + ∑ are depend on the customer type and the realized quantity of demand, so we can not estimate the size of the second part of the right-hand-side of equality (10) until the allocation decisions are made. Thus, α Δ is not necessarily positive or negative. It means that the traditional single- step upgrade allocation policy is not the optimal in this integrated system. Lemma 1. ()QΠ is concave in Q . Proof. The programming model can be simplified and transformed as, 1 i , , , () ( ) t nj ddk QEQ Π =Π i,, , ,, , , ()max[( ) ( ) ( )] tt i j i j ii jj i j ii j i j iii i i j ij i j i i j QyvdkfyCQfyheQIy α Π= − + − − − +− ∑∑∑∑∑ ∑ s.t. ,i j i i y d ≤ ∑ (11) ,i j ii i j y eQ I ≤ + ∑ (12) , , , , (1,2, , ) ij i y QRi j n + ∈∈ () i QΠ is a linear program model of Qi (i=1,…,n) with the constraints of inequalities (11) and (12). Obviously, () i QΠ is concave in Qi because a linear program is concave in variables that determine the right-hand-side of its constraints. Van Slyke and Wets (1966) prove that concavity is preserved over the expectation operator, so ()QΠ is concave in Qi. Because is a positive linear function in i Q , so ()QΠ , as the function of i Q , is also concave in Q (Rockafeller,1970). 5. Solution method and numerical experiment 5.1 Solution method The decision model is a stochastic programming model, the demand distributions for the products are modelled not by their analytic functions but rather by a finite number of randomly generated demand scenarios that are statistically identical to the joint probability distribution of the demands. It should be noted that a finite number of scenarios can model only an approximation of continuous distributions, but that a model with a sufficiently large Supply Chain Management 196 number of scenarios can approach the actual distributions. Let M denote the number of scenarios and superscript each of the following parameters and variables by the scenario index m: m i d and tm j k . Monte Carlo sampling is often used in stochastic linear program to maximize the expected profit over the scenarios. Each scenario may be given a probability weight wm. We now have the following formulation for the problem that models m i d and tm j k distributions using the M scenarios: ,, , , ,, , ()max[ ( ) ( ( )) ()] mtmtm i j i j mii m j ii j ij m i m j i iijijiiii ij ij Qywvdwkfy CQ fy heQ I y α ′ Π= − + −−−+− ∑∑∑∑∑∑ ∑∑ s.t. ,i jj i y d ≤ ∑ (13) ,i j ii i j y eQ I ≤ + ∑ (14) , ,, ij i y QR + ∈ 0m M < ≤ The solution steps for the objective function (3) are shown in figure 7. Fig. 7. The solution steps There are several basic steps to conduct the sample simulation. Step 1. Analysis the programming model, and determine the stochastic variables in the model. Step 2. Generate the stochastic samples. Step 3. Solve the model based on each sample series. Step 4. Determine the weight of each sample series. Capacity Collaboration in Semiconductor Supply Chain with Failure Risk and Long-term Profit 197 Step 5. Calculate the optimal value of the decision variables. In the simulation, the choice of the number of scenarios M is important when the scenarios in the model can only approximate the demand distributions. As the value of scenarios M increase, there is a trade-off between the increased computing time and the improved accuracy as a result of a better approximation of the model. 5.2 A simple numerical experiment Using the above formulation, we can obtain an optimal material quantity and the optimal capacity of each manufacture by solving the program. As an example, we consider a problem with five products (n=5) and the following are the parameters (see table 3.): Product p i v i e i h i I i u i 1 7 13 20 7 22 0.5 2 6 10 24 4 34 0.43 3 5 8 32 6 21 0.39 4 4 7 31 3 41 0.35 5 3 5 27 5 32 0.25 Table 3. The values of parameters We assume a= 3, b=2.4, C=2.3, M=5000, w m =1. The value of f i,j is shown in table 4. Demand 1 Demand 2 Demand 3 Demand 4 Demand 5 Product 1 0.01 0.02 0.021 0.024 0.028 Product 2 0.012 0.023 0.024 0.027 Product 3 0.01 0.013 0.017 Product 4 0.012 0.021 Product 5 0.009 Table 4. The value of f i,j In this example, we assume that the demands are normally distributed with the given mean and standard deviation: 1 ~(34,42)dn , 2 ~(53,69)dn , 3 ~(52,18)dn , 4 ~(73,37)dn 5 ~(64,15)dn . We also assume 1 j k (j=1,2,3,4,5) follows beta distribution, and tm i k is generated as follows (table 5.): 1 t k 2 t k 3 t k 4 t k 5 t k t=1 B (3,5) B (4,7) B (4,6) B (5,4) B (4,4) t=2 B (2,4)* 1 1 k B (2,2)* 1 2 k B (5,4)* 1 3 k B (2,9)* 1 4 k B (7,2)* 1 5 k t=3 1- 1 1 k - 2 1 k 1- 1 2 k - 2 2 k 1- 1 3 k - 2 3 k 1- 1 4 k - 2 4 k 1- 1 5 k - 2 5 k Table 5. The value of tm i k As has been studied in the theory of Monte Carlo sampling, 5000 iterations of simulation is enough to get a relatively accurate result. After 5000 iterations, we get the optimal material quantity Q=136.29. The optimal capacity of manufacturers are Q 1 =18.23, Q 2 =24.72, Q 3 =26.58, Q 4 =29.15, Q 5 =37.61. Supply Chain Management 198 6. Conclusion In this work we study a capacity determination problem of the manufacture and allocation integrated supply chain in semiconductor industry. The material supplier invests in materials (e.g. silicon) before the actual demands are known. All the manufacturers produce one type of output, but the nature performances of the outputs produced by different manufacturer are distinctive because of the different technical and equipment conditions. The outputs are classified to different products by the nature performances and then allocated to customers. Customers can be divided into three types (the positive customers, neutral customers and the conservative customers), and their long-term profit functions are different. The demands can be upgraded when a particular type of the product has been depleted. 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ISSN 0020-7543 [...]... |Attacks Weight Skimmi s ng Eavesdroppi MIM ng Physica Fraud l attack attack L1 0.9% 10.00 15.00 15.00 30.00 63 .90 L2 4.3% 11.01 11.01 13.21 17 .62 28.14 L3 8 .6% 21. 46 17.17 25. 76 25. 76 27.43 L4 86. 2% 21.41 21.41 26. 77 26. 77 17.10 Sum 100.0% 63 .9 64 .6 80.7 100.1 1 36. 6 445.9 14.3% 14.5% 18.1% 22.5% 30 .6% 1 Normalized Score Table 19 Operational Cost (OcA) Evaluation based on scores of test features for cloning... 102 0 0 102 16. 9% 19.1% 16. 9% 16. 9% 19.1% 11% 102 53.7 53.7 102 920.5 100.0% Table 21 Overall cost calculation for ten cloned attack Cost types| Cost matrice FN ADCost (fraud) Operational Cost ARCost(fraud) Penalty Sum Normalized Score 20.9 36. 6 0 20.9 20.9 20 36. 6 TP (∀ ∈ E’ SA) 20.9 TP (DCost ≥ Rcost) TP (DCost < Rcost) 36. 6 FP (DCost ≥ Rcost) 0 0 TN Sum 20.9 20.9 26 20 26 57.5 66 .9 46. 9 57.5 77.5... different attacks Features |Attacks L1 L2 L3 L4 Sum Normalized Score Weights Skimming Eavesdropping MIM 0.9% 4.3% 8 .6% 86. 2% 10.00 11.01 21. 46 21.41 15.00 11.01 17.17 21.41 15.00 13.21 25. 76 26. 77 Physical attack 10.00 8.81 17.17 21.41 100.0% 63 .9 64 .6 80.7 57.4 20.7% 20.9% 26. 1% 32.4% 266 .6 1 Table 14 Operational Cost (OcA) Evaluation based on scores of test features and cloning attacks types Test features... Importance of RFID components Attacks| Costs Weights Skimming Eavesdropping Tags Readers Database(local) 20.0% 15.0% 30.0% 35.0% 100.0% 6. 00 3.19 1.58 0.99 11.8 3.00 4.79 2. 36 3. 96 14.1 21.9% 26. 3% Network Sum Normalized Score MIM 5.00 6. 38 2. 76 3. 96 18.1 Physical attack 6. 00 1 .60 1.18 0.99 9.8 53.7 33.7% 18.2% 1 Table 8 Damage Cost (DcA) Evaluation based on scores of attacks and target resources factors... well as Response Costs than fraud attacks This occurs because a fraud attack is only part of a cloning attack A cloning attack needs to occur before a fraud attack can occur 224 Supply Chain Management Costs |Attacks Cloning Fraud Range Damage 1-100 53.7 36. 6 Response 53.7 25.8 1-100 Sum 107.4 62 .4 170.02 63 .2% 36. 8% 100% Normalized Score Table 18 Consequential Cost (CC) Evaluation for summation between... against the requested operation 5 Supply Chain (SC) partner authentication is done through a certificate authority (CA) service using our trust framework The partners that need to access the clone detector to provide their local certificate to the CA server installed in our trust framework 209 A Cost-based Model for Risk Management in RFID-Enabled Supply Chain Applications 6 The Object Naming Service (ONS)... 17.5% 26. 3% 35.0% 21.3% 100% Table 9 Criticality of RFID components in term of replacing, unavailability and disclosure for Response cost Attacks| Costs Weights Skimming Eavesdropping MIM Physical attack Tags Readers Database(local) Network Sum Normalized Score 20.0% 15.0% 30.0% 35.0% 100.0% 3.00 2.39 1.58 1.98 8.9 3.00 5.59 1.97 2.97 13.5 6. 00 6. 38 2. 76 3. 46 18 .6 8.00 1 .60 1.58 1.48 12.7 53.7 16. 7%... the attack requires less expertise and a lower Response Cost 222 Features |Attacks Features Time Sum Normalized Score Supply Chain Management Weights Skimming Eavesdropping 70.0% 30.0% 100.0% 19.2 0.9 20.0 19.4 2.0 21.4 19 .6% 21.0% MIM 24.2 2 .6 26. 8 Physical attack 30.3 3.5 33.8 102.0 26. 3% 33.1% 100.0% Table 15 Operational Cost (OcA) Evaluation based on weight for test features and time Fig 7 Overall... and cost insensitive models for both cloning and fraud attacks For instance, in a supply chain environment where both fraud and cloning are the act of counterfeiting, the total potential loss is estimated based on formula (1) in our model and is calculated to be US$ 169 2.90 If this cost sensitive model is 2 26 Supply Chain Management calculated for cloning attack for ‘skimming attack ’ for ten RFID tags,... trading partners create and store their own serialised information about each and every product in their own local EPC-IS The manufacturer manages and hosts a database that stores information about the generation of their products Trading partners manages their local EPC-IS and store information about products movement through the supply chain This local EPC-IS is accessible by all supply chain partners . of the demand substitution to the supply chain network. Substitution can help to Supply Chain Management 194 remit the bullwhip effect and gives the supply chain with flexibility. A number. optimal material quantity Q=1 36. 29. The optimal capacity of manufacturers are Q 1 =18.23, Q 2 =24.72, Q 3 = 26. 58, Q 4 =29.15, Q 5 =37 .61 . Supply Chain Management 198 6. Conclusion In this work. Trading partners manages their local EPC-IS and store information about products movement through the supply chain. This local EPC-IS is accessible by all supply chain partners. Each involved partner